Also working on pairs of consecutive fibonacci numbers (f_n, f_(n+1)) instead of the matrix [[f_(n+1) f_n] [f_n f_(n-1)]] makes this much simpler.

  def fib(n):
    def fib2(n):
      # returns (f_n, f_(n+1))
      if n == 0:
        return 0, 1
      if n % 2:
        a, b = fib2(n-1)
        return b, a+b
      a, b = fib2(n//2)
      return b*a + a*(b-a), a*a + b*b
    return fib2(n)[0]